Mathematical and statistical modeling techniques are relevant to biomedical investigations at a variety of scales and in a variety of contexts. Our Lab applies expertise in the mathematical, statistical and computing sciences to address novel problems arising in cutting edge areas of biomedical research. In a joint study with investigators in Laboratory of Molecular Biology, NCI and Institut National de la Recherche Agronomique (INRA), France, we are attacking the problem of protein structure classification, with the goal of improving automated methods for recognition and classification of protein domains in three dimensional structures. Domains are thought to be the building blocks of complex structures, and often determine protein function. Our current project compares two existing protein structure similarity detection methods (VAST and SHEBA) and contrasts them with a manually curated protein classification, SCOP. A large representative database of structures has been used to identify ambiguous classes of proteins which neither automated method effectively distinguishes. In a project with the Hormone Action and Oncogenesis Section, NCI, we provided a model and analysis paradigm for confocal fluorescence microscopy images of cell nuclei in metaphase and interphase. This procedure selectively labels specific chromosomes, and is being used to determine the underlying organization of chromosomes within the nuclei, with a view to chromosome translocation, in normal and cancer cells. Our approach uses geometric statistics to determine if the placement of genome territories in the nucleus of interphase cells, both respect to the nuclear center and with each other is significant statistically. We are particularly interested to see if placement of and correlations between territories affect gene expression or vary between cell types. With an investigator in the Division of International Epidemiology, Fogarty International Center, we have developed a phenomenological model of Plasmodium parasite/red blood cell dynamics, and have used it to examine the consequences of strategies of attack of the different Plasmodium species that attack humans. For example, we showed that P. vivax, which attacks red blood cells less than 36 hours old, would be very virulent without a strong immune response as even a barely aggressive infection will choke off the host?s supply of mature red blood cells even though the percentage of blood cells actually infected would be very small. At present we are studying the consequences of dual P. vivax- P. falciparum and P. malariae- P. falciparum infections, and are examining when P. falciparum (an attacker of red blood cells of any age) can facilitate production of parasites of the co-infecting Plasmodium species. Investigators in NICHD and CIT have created Extended Microcapture Dissection (or XMD), a major revision of the laser capture microdissection (LCM) device that was developed here at NIH in the mid 1990?s. In this new form of microtransfer using thermoplastic films, the intrinsic absorption of stained tissue heats up the polymer and causes it to melt and form a thermoplastic bond similar to that in LCM. We have performed thermal diffusion modeling to assist in optimizing the design or operations of this new device. Prototypes have been built and the focus is currently on the testing of prototypes. In a project with investigators in LIMB, NICHD related to the development of diffusion tensor MRI we used the Non-Uniform Rational B-Splines (NURBS) for extracting geometrical features of the basic brain anatomy. Ultimate goal is the development of the continuous tensor model based on NURBS, while currently only the special case fits can be obtained. In a project, with investigators of NIMH, multiple-electrode recordings from in-vitro neural network preparations are analyzed in order to deduce the underlying cortical network topology. The goal is to deduce general topological features from the observed avalanche dynamics. We obtained the results for the rat brain preparations, and conducted large scale simulations to verify those results. Current efforts are focused on developing a Bayesian framework for estimating the underlying network topology.